A and B are two sets such that n(A-B)=20+x, n(B-A)=3x and n(A ∩B)=x+1.Draw a Venn diagram to illustrate this information.Find (i)the value of x (ii)n(AUB)

In this question you have not given that n(A) = n(B).

Venn diagram:


n(a-b)=20+x

n(b-a)=3x

n(a  b) =x+1

We know that

n(a-b) = n(a)-n(a  b)

∴n(a) = n(a-b) + n(a  b)

= (20+x) + (x + 1)

= 2x + 21

Similarly, n(b) = n(b-a) + n(a  b)

=3x + (x+1)

=4x + 1

According to the question,

n(a) = n(b)

∴2x + 21 = 4x +1

⇒2x = 20

 x = 10

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